Question

A rectangular sheet of paper with length 20cm and breadth 10cm is to be cut into small squares of side 5cm each.
a. Find the area of one square piece?
b. Find the area of the rectangular sheet?
c. How many square pieces will be obtained?

Answer 1

Answer :-

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

Here the concept of Areas of Square and Areas of Rectangle has been used. We are already given dimensions of square and rectangle. So we can easily find out their Areas. Also, we know that sum of areas of every square piece will be equal to Area of Rectangular sheet. So, number of pieces will be the ratio of area of rectangular sheet by area of each square piece.

Let's do it !!

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★ Equations Used :-

$\\\;\boxed{\sf{Area\;of\;Square\;=\;\bf{(Side)^{2}}}}$

$\\\;\boxed{\sf{Area\;of\;Rectangle\;=\;\bf{Length\;\times\;Breadth}}}$

$\\\;\boxed{\sf{Number\;of\;Pieces\;=\;\bf{\dfrac{Area\;of\;Rectangular\;Sheet}{Area\;of\;each\;Square\;piece}}}}$

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★ Solution :-

Given,

» Length of Rectangular Piece = 20 cm

» Breadth of Rectangular Piece = 10 cm

» Side of each Square Piece = 5 cm

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a.) For the Area of each Square Piece :-

$\\\;\;\;\sf{:\rightarrow\;\;Area\;of\;Square_{(each\;piece)}\;=\;\bf{(Side)^{2}}}$

$\\\;\;\;\sf{:\rightarrow\;\;Area\;of\;Square_{(each\;piece)}\;=\;\bf{(5)^{2}}}$

$\\\;\;\;\bf{:\rightarrow\;\;Area\;of\;Square_{(each\;piece)}\;=\;\bf{25\;\;cm^{2}}}$

$\\\;\underline{\boxed{\tt{Area\;\;of\;\;Each\;\;Square\;\;Piece\;\;is\;\;\bf{25\;\;cm^{2}}}}}$

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b.) For the Area of Rectangular Sheet :-

$\\\;\;\;\sf{:\Longrightarrow\;\;Area\;of\;Rectangle\;=\;\bf{Length\;\times\;Breadth}}$

$\\\;\;\;\sf{:\Longrightarrow\;\;Area\;of\;Rectangle\;=\;\bf{20\;\times\;10}}$

$\\\;\;\;\bf{:\Longrightarrow\;\;Area\;of\;Rectangle\;=\;\bf{200\;\;cm^{2}}}$

$\\\;\underline{\boxed{\tt{Area\;\;of\;\;Rectangular\;\;Sheet\;\;is\;\;\bf{200\;\;cm^{2}}}}}$

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c.) For the Number of Square Pieces :-

$\\\;\;\;\sf{:\mapsto\;\;Number\;of\;Pieces\;=\;\bf{\dfrac{Area\;of\;Rectangular\;Sheet}{Area\;of\;each\;Square\;piece}}}$

$\\\;\;\;\sf{:\mapsto\;\;Number\;of\;Pieces\;=\;\bf{\dfrac{200}{25}}}$

$\\\;\;\;\sf{:\mapsto\;\;Number\;of\;Pieces\;=\;\bf{8}}$

$\\\;\underline{\boxed{\tt{Number\;\;of\;\;Square\;\;Pieces\;\;is\;\;\bf{8\;\;pieces}}}}$

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★ More to know :-

$\\\;\sf{\leadsto\;\;Area\;of\;Circle\;=\;\pi r^{2}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Triangle\;=\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

$\\\;\sf{\leadsto\;\;Area\;of\;Parallelogram\;=\;Base\;\times\;Height}$

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Circle\;=\;2\pi r}$

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Rectangle\;=\;2\;\times\;(Length\;+\;Breadth)}$

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Square\;=\;4\;\times\;Side}$

Answer 2

${\bold{\large{\underbrace{\sf{Understanding \: the \: question \: 1^{st}}}}}}$

This question says that there is a rectangular sheet of paper of length and breadth 20 cm and 10 cm respectively. Now this question says that the rectangular sheet of paper is cutted into small squares piece of sides 5 cm each. Now this question ask us to find the following well !

❖ Area of a square piece.

❖ Area of rectangular sheet.

❖ No. of square pieces will obtained.

${\bold{\large{\underline{\sf{Given \: that}}}}}$

✠ Length of rectangular sheet of paper = "20 cm".

✠ Breadth of rectangular sheet of paper = "10 cm".

✠ Sheet of paper is cutted into small squares of side "5 cm" each.

${\bold{\large{\underline{\sf{To \: find}}}}}$

✠ The area of one square piece.

✠ The area of the rectangular sheet.

✠ Number of square pieces will be obtained.

${\bold{\large{\underline{\sf{Solution}}}}}$

✠ The area of one square piece = 25 cm²

✠ The area of the rectangular sheet = 200² cm

✠ Number of square pieces will be obtained = 8

${\bold{\large{\underline{\sf{We \: also \: write \: these \: as}}}}}$

✠ Square as ²

✠ Length as l

✠ Breath as b

✠ Side as s

${\bold{\large{\underline{\sf{Using \: concepts}}}}}$

${\bold{\bf{\boxed{\leadsto \: Area \: of \: rectangle}}}}$

${\bold{\bf{\boxed{\leadsto \: Area \: of \: square}}}}$

${\bold{\bf{\boxed{\leadsto \: Number \: of \: square \: pieces}}}}$

${\bold{\large{\underline{\sf{Using \: formulas}}}}}$

${\bold{\bf{\boxed{\leadsto \: Area \: of \: rectangle \: = \: Length \: \times \: Breadth}}}}$

${\bold{\bf{\boxed{\leadsto \: Area \: of \: square \: = \: Side \: \times \: Side}}}}$

${\bold{\bf{\boxed{\leadsto \: Number \: of \: square \: pieces \: = \: \frac{Area \: of \: rectangular \: sheet}{Area \: of \: each \: square \: piece}}}}}$

${\bold{\large{\underline{\sf{Full \: solution}}}}}$

a.

${\bold{\sf{Area \: of \: square_{each \: piece} \: = \: Side \times \: Side}}}$

${\bold{\sf{Area \: of \: square_{each \: piece} \: = \: 5 \: \times \: 5}}}$

${\bold{\sf{Area \: of \: square_{each \: piece} \: = \: 25 \: cm^{2}}}}$

${\bold{\large{Hence \: area \: of \: each \: square \: piece = \rm \: 25 \: cm^{2}}}}$

b.

${\bold{\sf{Area \: of \: rectangle_{sheet} \: = \: Length \times \: Breadth}}}$

${\bold{\sf{Area \: of \: rectangle_{sheet} \: = \: 20 \: \times \: 10}}}$

${\bold{\sf{Area \: of \: rectangle_{sheet} \: = \: 200 \: cm{2}}}}$

${\bold{\large{Hence \: area \: of \: rectangular \: sheet = \rm \: 200 \: cm^{2}}}}$

c.

${\bold{\sf{Number \: of \: square \: pieces \: = \: \frac{Area \: of \: rectangular \: sheet}{Area \: of \: each \: square \: piece}}}}$

${\bold{\sf{Number \: of \: square \: pieces \: = \: \frac{200^{2}}{25^{2}}}}}$

${\bold{\sf{Number \: of \: square \: pieces \: = \: \frac{200}{25}}}}$

${\bold{\sf{Number \: of \: square \: pieces \: = \: 8}}}$

${\bold{\large{Number \: of \: square \: pieces \: = \rm \: 8 \: pieces}}}$

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